A newly devised filter and its application to signal and image processing

A filter, called Recursive Approaching Signal Filter (RASF), is mathematically derived based on a recursive computation of the previous filtering output. In this computation, for every window each pixel or centered point is exponentially weighted more if it is closer to the output of the previous filtering operation. These iterations bring the sequence to convergence to a fixed point. This is the RASF filter. This robust filter combines many advantages of most linear, nonlinear and adaptive filters, and makes no assumptions about the type of signal or noise.; The RASF can be mathematically expressed as {dollar}{dollar}{bsol}cases{lcub}W{bsol}sb{lcub}k{rcub}(x)=e{bsol}sp{lcub}-{bsol}alpha{bsol}vert R{bsol}sb{lcub}k{rcub}-f(x){bsol}vert{rcub}{bsol}cr{bsol}cr R{bsol}sb{lcub}k+1{rcub}={lcub}{bsol}int{bsol}sbsp{lcub}-w/2{rcub}{lcub}w/2{rcub}W{bsol}sb{lcub}k{rcub}(x)f(x)dx{bsol}over {bsol}int{bsol}sbsp{lcub}-w/2{rcub}{lcub}w/2{rcub}W{bsol}sb{lcub}k{rcub}(x)dx{rcub}{bsol}cr{rcub}{dollar}{dollar}; A mathematical derivation has been given for the convergence of this recursive relationship. Further the last output of the RASF is shown to be independent of the initial value.; The RASF is applied to geophysical data processing. A new algorithm for separation of up-going and down-going wave modes in VSP data processing is proposed that uses the RASF. When this new algorithm is applied to model and field VSP data, it obtains the up-going wave modes and removes noise very well. The RASF is also applied to separation of superimposed anomalies such as regional and local gravity anomalies. This new filter overcomes many of the disadvantages associated with spectrum overlap that are present in other filters and thus performs well in separating the superimposed signal, eliminating inhomogeneous distortion and removing noise.; The RASF is also applied to image processing. This filter makes no assumptions on the type of signal or noise and also preserves much of the high frequency signal. Therefore, the filter passes step functions well without altering them. This allows for the processed image results of the RASF to have excellent visual quality.; In each of the cases relating to geophysical data and image processing, the RASF is compared to other filters commonly used for a given purpose such as the median, moving average, Wiener and adaptive Wiener filters. Quantitative evaluations are given for VSP and image processing as well as visual comparisons.